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 A006157 a(n+1) = (n-1)*a(n) + n*n!. (Formerly M3950) 6
 1, 5, 28, 180, 1320, 10920, 100800, 1028160, 11491200, 139708800, 1836172800, 25945920000, 392302310400, 6320426112000, 108101081088000, 1956280854528000, 37347179950080000, 750144785854464000, 15813863053148160000, 349121438173347840000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS Number of ascending runs of length at least two in all permutations of [n]. Example: a(3)=5 because we have (123), (13)2, 3(12), 2(13), (23)1 and 321, where the ascending runs of length at least 2 are shown between parentheses. - Emeric Deutsch and Ira M. Gessel, Sep 07 2004 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS J. Francon, Histoires de fichiers, RAIRO Informatique ThÃ©orique et Applications, 12 (1978), 49-62. J. Francon, Histoires de fichiers, RAIRO Informatique ThÃ©orique et Applications, 12 (1978), 49-62. (Annotated scanned copy) FORMULA a(n) = (2n-1)/6 * n!. E.g.f.: x^2*(3-x)/(6*(1-x)^2). - Emeric Deutsch and Ira M. Gessel, Sep 07 2004 MATHEMATICA Table[(2n-1)/6*n!, {n, 2, 30}] (* Harvey P. Dale, Jan 06 2014 *) CROSSREFS Cf. A014484. Sequence in context: A082031 A020081 A095676 * A179326 A156629 A123776 Adjacent sequences:  A006154 A006155 A006156 * A006158 A006159 A006160 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Harvey P. Dale, Jan 06 2014 STATUS approved

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Last modified December 18 20:06 EST 2018. Contains 318245 sequences. (Running on oeis4.)